What is the integral from 1 to 4 of 8x^3-2x+e^x ?

The integral from 1 to 4 of 8x^3-2x+e^x is e^4-e+495

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integral from 1 to 4 of 8x^3-2x+e^x

\int_{1}^{4} 8 x^{3} - 2 x + e^{x} d x

e^{4} - e + 495

Decimal

546.87986 \dots

Solution steps

\int_{1}^{4} 8 x^{3} - 2 x + e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} 8 x^{3} d x - \int_{1}^{4} 2 x d x + \int_{1}^{4} e^{x} d x

\int_{1}^{4} 8 x^{3} d x = 510

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} e^{x} d x = e^{4} - e

= 510 - 15 + e^{4} - e

Simplify

= e^{4} - e + 495

What is the integral from 1 to 4 of 8x^3-2x+e^x ?
The integral from 1 to 4 of 8x^3-2x+e^x is e^4-e+495